A coil is joined in series with a pure resisttor
When a coil (also known as an inductor) is joined in series with a pure resistor in an electric circuit, it forms a series RL circuit. In this type of circuit, both the inductor and the resistor are connected end to end, sharing the same current.
In order to determine the behavior of a series RL circuit, you need to consider the following elements:
1. Resistance (R): The resistor in the circuit produces a voltage drop proportional to the current flowing through it, according to Ohm's law (V = IR). The resistance is measured in ohms (Ω).
2. Inductance (L): The inductor in the circuit opposes changes in current by generating a counter electromotive force (emf) according to Faraday's law. The inductance is measured in henries (H).
To analyze a series RL circuit, you can follow these steps:
Step 1: Determine the values of the resistance (R) and inductance (L).
Step 2: Calculate the time constant (τ) of the circuit. The time constant is the inductance divided by the resistance (τ = L/R). It represents the time it takes for the current in the circuit to reach approximately 63% (1 - e^(-1)) of its final steady-state value.
Step 3: Determine the behavior of the circuit based on the time constant:
- If the time constant is small compared to the time scale of the circuit's operation, the inductor is considered as a short circuit, and the circuit behaves as a purely resistive circuit.
- If the time constant is large compared to the time scale of the circuit's operation, the inductor is considered as an open circuit, and the circuit behaves as a purely inductive circuit.
- If the time constant is neither significantly small nor large, the circuit exhibits a transient behavior until it reaches its steady-state.
Step 4: Calculate the impedance (Z) of the circuit using the resistance (R) and inductance (L). The impedance is the effective opposition to the flow of an alternating current (AC) and is measured in ohms (Ω).
The impedance of a series RL circuit can be calculated by the formula:
Z = sqrt(R^2 + (ωL)^2)
Where ω is the angular frequency, given by ω = 2πf, and f is the frequency of the AC source.
By analyzing the impedance, you can determine how the circuit responds to different frequencies of the AC source. For example, when the frequency is at the resonant frequency, the impedance reaches its minimum value, and the circuit is said to be in resonance.
In summary, in a series RL circuit, the coil (inductor) and the resistor are connected in series. The circuit's behavior is determined by the values of resistance (R) and inductance (L), as well as the frequency of the AC source. To fully analyze the circuit, you need to calculate the time constant and impedance, considering the different scenarios based on the time constant.